Query about Question 5 from "PrepSwift: # of Numbers in Factorials II" [12368]

Link: https://prepswift.gregmat.com/quizzes/quiz/of-numbers-in-factorials-ii-quiz (Question 5)


I don’t understand the solution at all. Can someone explain this please

This question is equivalent to finding the number of primes that are factors of 36! . Maybe that provides you with a nudge in the right direction.

I found this question particularly tricky. Should the tutorial material have been enough for me to have the tools to answer this question? Because I didn’t feel so.

I have been finding the tutorials and test questions on Adding Numbers to Multiples, Sum of Multiples in an Interval, Number of Numbers in Factorials extremely difficult to follow. The concepts have been nearly impossible to grasp without help from other online sources – like for example, there’s a pretty straightforward way to find the number of of a certain number in Factorials and that is by using Legendre’s formula. I understand the need for explaining the entire method, but it would make concepts much clearer if after explaining each part of the method, the generalised formula is reiterated.

The videos for these topics also seemed very rushed, missing out on key points needed to explain the concepts better.

Just for context, the videos on these topics are around 20-30 minutes long but it took me 5-6 hours of pausing, rewatching, going through explanations over and over to completely grasp these concepts.

This is done in Part 3.